Chapter 18 Mirrors and Lenses

Demonstration Game

How big does a full length mirror need to be?

Mirror Game

x x y 2y

Chapter 18 Mirrors and Lenses Kiara getting ready to put on her band-aid

Chapter 18 Mirrors and Lenses

The simpler method relies on two simple rules of reflection for concave mirrors. They are: Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection. Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection.

Chapter 18 Mirrors and Lenses 1. Pick a point on the top of the object and draw two incident rays traveling towards the mirror. 2. Using a straight edge, accurately draw one ray so that it passes exactly through the focal point on the way to the mirror. Draw the second ray such that it travels exactly parallel to the principal axis. Place arrowheads upon the rays to indicate their direction of travel. The method of drawing ray diagrams for concave mirror is described below. The description is applied to the task of drawing a ray diagram for an object located beyond the center of curvature (C) of a concave mirror. The radius of curvature C is twice the focal length (F).

Chapter 18 Mirrors and Lenses Any ray parallel reflects through the focus Any ray through the focus reflects back parallel

Chapter 18 Mirrors and Lenses

d o Object Distance d i Image Distance f Focal Length F Focal Point Ray diagrams

Chapter 18 Mirrors and Lenses Describing Images 1.Virtual/Real 2.Inverted/Erect 3.Magnified/Reduced

Chapter 18 Mirrors and Lenses

The diagrams above shows that in each case, the image is located behind the convex mirror a virtual image an upright image reduced in size (i.e., smaller than the object) Chapter 18 Mirrors and Lenses

Diverging/Convex mirror Converging/Concave mirror

Images formed by a converging spherical mirror Characteristics a) Distant object Real Inverted Reduced At F b) Object beyond C Real Inverted Smaller Between C and F c) Object at C Real Inverted Same size At C

Images formed by a converging spherical mirror Characteristics d) Object between F and V Virtual Erect Larger Behind mirror e) Object at F No image Reflected rays are parallel f) Object anywhere Virtual Erect Smaller Behind mirror between F and V Images formed by a diverging spherical mirror

Chapter 18 Mirrors and Lenses A 5.0-cm tall light bulb is placed a distance of 45 cm from a concave mirror having a focal length of 15 cm. Determine the image distance and the image size. Describe the image

Chapter 18 Mirrors and Lenses 1/f = 1/do + 1/d i 1/(15 cm) = 1/(45 cm) + 1/d i 1/(15 cm) – 1/(45 cm) = 1/d i 3/45 – 1/45 = 1/d i 2/45 = 1/d i d i = 22.5 cm

Chapter 18 Mirrors and Lenses M = - d i /d o M = -22.5/45 M = - ½ S i = -1/2 (5 cm) Si = -2.5 cm The image is real, reduced, and inverted.

Apparatus Image Concave Mirror Concave Mirror Concave Mirror Concave Mirror Concave Mirror Convex Mirror Beyond 2F At F Between 2F and F At 2F Between 2F and F Between F and the Lens Large or Small Virtual or Real Inverted or Erect Position Mirror Table SmallRealInvertedBetween F and 2F SameRealInverted At 2F LargeRealInverted Beyond 2F None LargeVirtualErect Behind the Mirror SmallVirtualErect Behind the Mirror Object Location

SmallRealInvertedBetween F and 2F SameRealInverted At 2F LargeRealInverted Beyond 2F None LargeVirtualErect Behind the Mirror SmallVirtualErect Behind the Mirror A D F E C B

Types of Lenses

Chapter 18 Mirrors and Lenses Converging/Convex lens Thicker in the middle and thinner on top Diverging/Concave lens Thicker on the top and thinner in the middle d o is positive for real objects d i is positive for real images d i is negative for virtual images f is positive for convex lenses f is negative for concave lenses real images are in front of the mirror and behind the lens

Chapter 18 Mirrors and Lenses Any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point (i.e., in a direction such that its extension will pass through the focal point). Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. An incident ray which passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens. Lens Diagrams

Chapter 18 Mirrors and Lenses

Ray diagrams

Images formed by a converging lens Characteristics a) Distant object Real Inverted Smaller At F b) Object at 2F Real Inverted Same size At 2F c) Object between 2F and F Real Inverted Larger Beyond 2F

d) Object at F No image Refracted rays are parallel e) Object between F and lens Virtual Erect Larger Behind the object Image formed by a diverging lens f) Object anywhere Characteristics Virtual Erect Smaller Between object and lens

Chapter 18 Mirrors and Lenses

SmallReal Inverted Between F and 2F SameRealInverted At 2F LargeRealInverted Beyond 2F None Large VirtualErect Beyond the lens SmallVirtualErect Between the object & lens D F C A B E Anywhere

Chapter 18 Mirrors and Lenses Converging/Convex lens Thicker in the middle and thinner on top Diverging/Concave lens Thicker on the top and thinner in the middle d o is positive for real objects d i is positive for real images d i is negative for virtual images f is positive for convex lenses f is negative for concave lenses real images are in front of the mirror and behind the lens

P F FG B D ff A dodo didi soso sisi O Derivation of the Lensmaker’s Equation

P F FG B D ff A dodo didi soso sisi O substitute Multiply across

P F FG B D ff A dodo didi soso sisi O divide by d O d i f cancel out like terms